A generalized inhomogeneous coupled nonlinear Schrödinger system, which has certain applications in nonlinear optics or Bose–Einstein condensation, is investigated. The bilinear form and bilinear Bäcklund transformation are obtained via the Hirota method.
-soliton solutions are derived, and we graphically investigate the effects of the time-dependent coefficients on the solitons and their interactions. Physical quantities, such as the amplitude, width, velocity, and energy, are also derived. We see that the time-dependent coefficients have no influence on the amplitude of the soliton. With the changes in the amplitudes, the two solitons can, respectively, be enhanced and suppressed after the interaction. Interactions between the two cubic and two periodic solitons are also derived. The interactions are inelastic.